Assume that a simple random sample has been selected from a normally distributed population and test the given claim. identify the null and alternative hypotheses, test statistic, p-value, and state the final conclusion that addresses the original claim. in a manual on how to have a number one song, it is stated that a song must be no longer than 210 seconds. a simple random sample of 40 current hit songs results in a mean length of 234.1 sec and a standard deviation of 54.52 sec. use a 0.05 significance level and the accompanying minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. what do these results suggest about the advice given in the manual?

There is enough evidence to conclude that the sample is from a population of songs with a mean greater than 210 sec.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 210 seconds

Sample mean, = 234.1 sec

Sample size, n = 40

Sample standard deviation, s = 54.52 sec

First, we design the null and the alternate hypothesis

We use one-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

We calculate the p-value with the help of standard normal table.

P-value = 0.004005

Since,                    

We fail to accept the null hypothesis and accept the alternate hypothesis.

Thus, there is enough evidence to conclude that the sample is from a population of songs with a mean greater than 210 sec.

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